Question

How do you write an equation in standard form given (-3, -3), (7,2)?

Answer 1

`x-2y=3`

Explanation:

Just so we know what our target is:
Standard form for a linear equation is
`color(white)("XXX")Ax+By=C`

Step 1: write the equation in slope-point form

slope: `m=(Delta y)/(Delta x) = (2-(-3))/(7-(-3)) = 5/10 = 1/2`

slope point form with slope `m` through a point `(barx,bary)` is
`color(white)("XXX")(y-bary) = m(x-barx)`
Using the above slope and `(-3,-3)` for `(barx,bary)`
`color(white)("XXX")y+3 = 1/2(x+3)`

Step 2: convert from slope-point to standard form

`y+3=1/2(x+3)`

`rarr 2y+6 = x+3`

`rarr x-2y=3` `color(white)("XXX")`or if you want to be picky: `1x+(-2)y=3`